 Axiomatization of an exponential similarity functionAntoine Billot, Itzhak Gilboa and David Schmeidler PSE-Ecole d'économie de Paris (Postprint) from HAL Abstract: An individual is asked to assess a real-valued variable y based on certain characteristics x = (x1,..., xm), and on a database consisting of n observations of (x1,..., xm, y). A possible approach to combine past observations of x and y with the current values of x to generate an assessment of y is similarity-weighted averaging. It suggests that the predicted value of y, yn+1s, be the weighted average of all previously observed values yi, where the weight of yi is the similarity between the vector xn+11,..., xn+1m, associated with yn+1, and the previously observed vector, xi1,..., xim. This paper axiomatizes, in terms of the prediction yn+1, a similarity function that is a (decreasing) exponential in a norm of the difference between the two vectors compared. Keywords: Similarity function; Axiom; Exponential decay (search for similar items in EconPapers) Published in Mathematical Social Sciences, 2008, Vol.55,n°2, pp.107-115. ⟨10.1016/j.mathsocsci.2007.08.002⟩ There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:pseptp:hal-00463265 DOI: 10.1016/j.mathsocsci.2007.08.002 Access Statistics for this paper More papers in PSE-Ecole d'économie de Paris (Postprint) from HAL |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.